<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Brás</style></author><author><style face="normal" font="default" size="100%">G. Eichfelder</style></author><author><style face="normal" font="default" size="100%">Júdice, J.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Copositivity tests based on the Linear Complementarity Problem</style></title><secondary-title><style face="normal" font="default" size="100%">Computational Optimization and Applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://link.springer.com/article/10.1007/s10589-015-9772-2</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">63</style></volume><pages><style face="normal" font="default" size="100%">461-- 493</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We present copositivity tests based on new necessary and sufficient conditions which require the solution of linear complementarity problems (LCP). We propose methodologies involving Lemke’s method, an enumerative algorithm and a linear mixed-integer programming formulation to solve the required LCPs. Moreover, we discuss a new necessary condition for (strict) copositivity based on solving a linear program, which can be used as a preprocessing step. The algorithms with these three different variants are thoroughly applied to test matrices from the literature and to max-clique instances with matrices of order up to 496×496. We compare our procedures with three other copositivity tests from the literature as well as with a general global optimization solver. The numerical results are very promising and equally good and in many cases better than the results reported elsewhere.&lt;/p&gt;
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